{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np # 数据处理最重要的模块\n",
    "import pandas as pd # 数据处理最重要的模块\n",
    "import scipy.stats as stats # 统计模块\n",
    "import scipy\n",
    "# import pymysql  # 导入数据库模块\n",
    "\n",
    "from datetime import datetime # 时间模块\n",
    "import statsmodels.formula.api as smf  # OLS regression\n",
    "\n",
    "# import pyreadr # read RDS file\n",
    "\n",
    "from matplotlib import style\n",
    "import matplotlib.pyplot as plt  # 画图模块\n",
    "import matplotlib.dates as mdates\n",
    "\n",
    "from matplotlib.font_manager import FontProperties # 作图中文\n",
    "from pylab import mpl\n",
    "#mpl.rcParams['font.sans-serif'] = ['SimHei']\n",
    "#plt.rcParams['font.family'] = 'Times New Roman'\n",
    "\n",
    "#输出矢量图 渲染矢量图\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "\n",
    "from IPython.core.interactiveshell import InteractiveShell # jupyter运行输出的模块\n",
    "\n",
    "#显示每一个运行结果\n",
    "InteractiveShell.ast_node_interactivity = 'all'\n",
    "\n",
    "#设置行不限制数量\n",
    "#pd.set_option('display.max_rows',None)\n",
    "\n",
    "#设置列不限制数量\n",
    "pd.set_option('display.max_columns', None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MarketR</th>\n",
       "      <th>MarketR_e</th>\n",
       "      <th>rfmonth</th>\n",
       "      <th>ret</th>\n",
       "      <th>ret_e</th>\n",
       "      <th>marketret3</th>\n",
       "      <th>marketret6</th>\n",
       "      <th>marketret12</th>\n",
       "      <th>Q</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1991-01-31</th>\n",
       "      <td>0.029998</td>\n",
       "      <td>0.036554</td>\n",
       "      <td>0.006930</td>\n",
       "      <td>0.023068</td>\n",
       "      <td>0.029624</td>\n",
       "      <td>-0.084127</td>\n",
       "      <td>-0.305662</td>\n",
       "      <td>0.254049</td>\n",
       "      <td>1991 Q1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-02-28</th>\n",
       "      <td>0.010203</td>\n",
       "      <td>0.021860</td>\n",
       "      <td>0.006930</td>\n",
       "      <td>0.003273</td>\n",
       "      <td>0.014930</td>\n",
       "      <td>-0.183573</td>\n",
       "      <td>-0.384745</td>\n",
       "      <td>0.241492</td>\n",
       "      <td>1991 Q1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-03-31</th>\n",
       "      <td>-0.099663</td>\n",
       "      <td>-0.060425</td>\n",
       "      <td>0.006930</td>\n",
       "      <td>-0.106593</td>\n",
       "      <td>-0.067355</td>\n",
       "      <td>-0.252928</td>\n",
       "      <td>-0.445049</td>\n",
       "      <td>0.288857</td>\n",
       "      <td>1991 Q1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-04-30</th>\n",
       "      <td>-0.079652</td>\n",
       "      <td>-0.031449</td>\n",
       "      <td>0.006651</td>\n",
       "      <td>-0.086303</td>\n",
       "      <td>-0.038100</td>\n",
       "      <td>-0.234776</td>\n",
       "      <td>-0.394937</td>\n",
       "      <td>0.691749</td>\n",
       "      <td>1991 Q2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-05-31</th>\n",
       "      <td>-0.074521</td>\n",
       "      <td>0.005375</td>\n",
       "      <td>0.006092</td>\n",
       "      <td>-0.080613</td>\n",
       "      <td>-0.000717</td>\n",
       "      <td>-0.236294</td>\n",
       "      <td>0.181673</td>\n",
       "      <td>1.542701</td>\n",
       "      <td>1991 Q2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>-0.031468</td>\n",
       "      <td>-0.033685</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>-0.032586</td>\n",
       "      <td>-0.034803</td>\n",
       "      <td>0.151050</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2024 Q3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.195992</td>\n",
       "      <td>0.227078</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>0.194874</td>\n",
       "      <td>0.225960</td>\n",
       "      <td>0.200147</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2024 Q3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-10-31</th>\n",
       "      <td>-0.003409</td>\n",
       "      <td>0.070220</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>-0.004527</td>\n",
       "      <td>0.069102</td>\n",
       "      <td>0.000228</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2024 Q4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-30</th>\n",
       "      <td>0.009724</td>\n",
       "      <td>0.045312</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>0.008606</td>\n",
       "      <td>0.044194</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2024 Q4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-31</th>\n",
       "      <td>-0.002679</td>\n",
       "      <td>-0.040799</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>-0.003797</td>\n",
       "      <td>-0.041917</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2024 Q4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>408 rows × 9 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             MarketR  MarketR_e   rfmonth       ret     ret_e  marketret3  \\\n",
       "month                                                                       \n",
       "1991-01-31  0.029998   0.036554  0.006930  0.023068  0.029624   -0.084127   \n",
       "1991-02-28  0.010203   0.021860  0.006930  0.003273  0.014930   -0.183573   \n",
       "1991-03-31 -0.099663  -0.060425  0.006930 -0.106593 -0.067355   -0.252928   \n",
       "1991-04-30 -0.079652  -0.031449  0.006651 -0.086303 -0.038100   -0.234776   \n",
       "1991-05-31 -0.074521   0.005375  0.006092 -0.080613 -0.000717   -0.236294   \n",
       "...              ...        ...       ...       ...       ...         ...   \n",
       "2024-08-31 -0.031468  -0.033685  0.001118 -0.032586 -0.034803    0.151050   \n",
       "2024-09-30  0.195992   0.227078  0.001118  0.194874  0.225960    0.200147   \n",
       "2024-10-31 -0.003409   0.070220  0.001118 -0.004527  0.069102    0.000228   \n",
       "2024-11-30  0.009724   0.045312  0.001118  0.008606  0.044194         NaN   \n",
       "2024-12-31 -0.002679  -0.040799  0.001118 -0.003797 -0.041917         NaN   \n",
       "\n",
       "            marketret6  marketret12        Q  \n",
       "month                                         \n",
       "1991-01-31   -0.305662     0.254049  1991 Q1  \n",
       "1991-02-28   -0.384745     0.241492  1991 Q1  \n",
       "1991-03-31   -0.445049     0.288857  1991 Q1  \n",
       "1991-04-30   -0.394937     0.691749  1991 Q2  \n",
       "1991-05-31    0.181673     1.542701  1991 Q2  \n",
       "...                ...          ...      ...  \n",
       "2024-08-31         NaN          NaN  2024 Q3  \n",
       "2024-09-30         NaN          NaN  2024 Q3  \n",
       "2024-10-31         NaN          NaN  2024 Q4  \n",
       "2024-11-30         NaN          NaN  2024 Q4  \n",
       "2024-12-31         NaN          NaN  2024 Q4  \n",
       "\n",
       "[408 rows x 9 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 导入市场回报率数据\n",
    "from pandas.tseries.offsets import MonthEnd\n",
    "Market_ret = pd.read_csv('F:/Python2025/python/datasets/Marketret_mon_stock2024.csv')\n",
    "Market_ret['month'] = pd.to_datetime(Market_ret['month'], format='%b %Y') + MonthEnd(0)\n",
    "Market_ret.set_index('month', inplace=True)\n",
    "Market_ret.sort_index(inplace=True)\n",
    "Market_ret = Market_ret.drop(columns=['Unnamed: 0'])\n",
    "Market_ret"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>cpi</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1987-01-31</th>\n",
       "      <td>5.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1987-02-28</th>\n",
       "      <td>5.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1987-03-31</th>\n",
       "      <td>5.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1987-04-30</th>\n",
       "      <td>6.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1987-05-31</th>\n",
       "      <td>7.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-03-31</th>\n",
       "      <td>-0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-04-30</th>\n",
       "      <td>-0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-05-31</th>\n",
       "      <td>-0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-06-30</th>\n",
       "      <td>0.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2025-07-31</th>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>463 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            cpi\n",
       "month          \n",
       "1987-01-31  5.1\n",
       "1987-02-28  5.4\n",
       "1987-03-31  5.8\n",
       "1987-04-30  6.7\n",
       "1987-05-31  7.6\n",
       "...         ...\n",
       "2025-03-31 -0.1\n",
       "2025-04-30 -0.1\n",
       "2025-05-31 -0.1\n",
       "2025-06-30  0.1\n",
       "2025-07-31  0.0\n",
       "\n",
       "[463 rows x 1 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inflation = pd.read_csv('F:/Python2025/python/datasets/inflation.csv')\n",
    "inflation['month'] = pd.to_datetime(inflation['month'],format='%Y/%m/%d')\n",
    "inflation.set_index('month',inplace=True)\n",
    "inflation.sort_values(by=['month'],axis=0,ascending=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>RV</th>\n",
       "      <th>RV1</th>\n",
       "      <th>RV2</th>\n",
       "      <th>RV3</th>\n",
       "      <th>var</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-12-31</th>\n",
       "      <td>0.011709</td>\n",
       "      <td>0.030732</td>\n",
       "      <td>0.046608</td>\n",
       "      <td>0.058424</td>\n",
       "      <td>0.000395</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-01-31</th>\n",
       "      <td>0.000690</td>\n",
       "      <td>0.001566</td>\n",
       "      <td>0.002593</td>\n",
       "      <td>0.003461</td>\n",
       "      <td>0.000030</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-02-28</th>\n",
       "      <td>0.000418</td>\n",
       "      <td>0.000707</td>\n",
       "      <td>0.000853</td>\n",
       "      <td>0.000763</td>\n",
       "      <td>0.000024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-03-31</th>\n",
       "      <td>0.001229</td>\n",
       "      <td>0.002925</td>\n",
       "      <td>0.004650</td>\n",
       "      <td>0.006369</td>\n",
       "      <td>0.000014</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-04-30</th>\n",
       "      <td>0.000855</td>\n",
       "      <td>0.001973</td>\n",
       "      <td>0.003364</td>\n",
       "      <td>0.004531</td>\n",
       "      <td>0.000010</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>0.000881</td>\n",
       "      <td>0.000823</td>\n",
       "      <td>0.000487</td>\n",
       "      <td>0.000487</td>\n",
       "      <td>0.000040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.012481</td>\n",
       "      <td>0.023868</td>\n",
       "      <td>0.034838</td>\n",
       "      <td>0.041347</td>\n",
       "      <td>0.000593</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-10-31</th>\n",
       "      <td>0.011652</td>\n",
       "      <td>0.007954</td>\n",
       "      <td>0.006707</td>\n",
       "      <td>0.006707</td>\n",
       "      <td>0.000685</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-30</th>\n",
       "      <td>0.004019</td>\n",
       "      <td>0.004118</td>\n",
       "      <td>0.005938</td>\n",
       "      <td>0.003775</td>\n",
       "      <td>0.000201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-31</th>\n",
       "      <td>0.001713</td>\n",
       "      <td>0.001517</td>\n",
       "      <td>0.001623</td>\n",
       "      <td>0.001167</td>\n",
       "      <td>0.000082</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>409 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                  RV       RV1       RV2       RV3       var\n",
       "month                                                       \n",
       "1990-12-31  0.011709  0.030732  0.046608  0.058424  0.000395\n",
       "1991-01-31  0.000690  0.001566  0.002593  0.003461  0.000030\n",
       "1991-02-28  0.000418  0.000707  0.000853  0.000763  0.000024\n",
       "1991-03-31  0.001229  0.002925  0.004650  0.006369  0.000014\n",
       "1991-04-30  0.000855  0.001973  0.003364  0.004531  0.000010\n",
       "...              ...       ...       ...       ...       ...\n",
       "2024-08-31  0.000881  0.000823  0.000487  0.000487  0.000040\n",
       "2024-09-30  0.012481  0.023868  0.034838  0.041347  0.000593\n",
       "2024-10-31  0.011652  0.007954  0.006707  0.006707  0.000685\n",
       "2024-11-30  0.004019  0.004118  0.005938  0.003775  0.000201\n",
       "2024-12-31  0.001713  0.001517  0.001623  0.001167  0.000082\n",
       "\n",
       "[409 rows x 5 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 导入日度市场回报率数据并计算已实现波动率\n",
    "Market_ret_day = pd.read_excel('F:/Python2025/python/datasets/Marketret_day_stock2024.xlsx')\n",
    "Market_ret_day['Day'] = pd.to_datetime(Market_ret_day['Day'],format='%Y-%m-%d')\n",
    "Market_ret_day.set_index('Day',inplace=True)\n",
    "Market_ret_day.sort_index(inplace=True)\n",
    "\n",
    "# Calculate monthly realized variance (RV) by summing squared excess returns\n",
    "Market_variance = Market_ret_day.resample('ME').apply(lambda df: pd.Series({\n",
    "    'RV': (df['er']**2).sum(),\n",
    "    'RV1': (df['er']**2).sum() + 2*(df['er']*df['er1']).sum(),\n",
    "    'RV2': (df['er']**2).sum() + 2*(df['er']*df['er1']).sum() + 2*(df['er']*df['er2']).sum(),\n",
    "    'RV3': (df['er']**2).sum() + 2*(df['er']*df['er1']).sum() + 2*(df['er']*df['er2']).sum() + 2*(df['er']*df['er3']).sum()\n",
    "}))\n",
    "\n",
    "Market_variance['var'] = Market_ret_day.resample('ME')['er'].var()\n",
    "Market_variance.index.name = 'month'\n",
    "\n",
    "# if RV3 <0, set to RV2 if RV2 <0, set to RV1 if RV1 <0, set to RV\n",
    "Market_variance['RV1'] = Market_variance['RV1'].where(Market_variance['RV1']>=0, Market_variance['RV'])\n",
    "Market_variance['RV2'] = Market_variance['RV2'].where(Market_variance['RV2']>=0, Market_variance['RV1'])\n",
    "Market_variance['RV3'] = Market_variance['RV3'].where(Market_variance['RV3']>=0, Market_variance['RV2'])\n",
    "Market_variance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>pb</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-12-31</th>\n",
       "      <td>1.886568</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-01-31</th>\n",
       "      <td>2.080065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-02-28</th>\n",
       "      <td>1.949285</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-03-31</th>\n",
       "      <td>1.560324</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-04-30</th>\n",
       "      <td>1.970330</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>0.097936</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.275764</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-10-31</th>\n",
       "      <td>0.254341</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-30</th>\n",
       "      <td>0.263924</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-31</th>\n",
       "      <td>0.261665</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>409 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                  pb\n",
       "month               \n",
       "1990-12-31  1.886568\n",
       "1991-01-31  2.080065\n",
       "1991-02-28  1.949285\n",
       "1991-03-31  1.560324\n",
       "1991-04-30  1.970330\n",
       "...              ...\n",
       "2024-08-31  0.097936\n",
       "2024-09-30  0.275764\n",
       "2024-10-31  0.254341\n",
       "2024-11-30  0.263924\n",
       "2024-12-31  0.261665\n",
       "\n",
       "[409 rows x 1 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 导入价格比率数据\n",
    "price_dividend = pd.read_csv('F:/Python2025/python/datasets/Price_dividend_mon2024.csv')\n",
    "price_dividend['month'] = pd.date_range(start='1990-12-31', end='2024-12-31', freq='ME')\n",
    "price_dividend.set_index('month', inplace=True)\n",
    "price_dividend.sort_index(inplace=True)\n",
    "price_dividend = price_dividend.drop(columns=['Unnamed: 0'])\n",
    "\n",
    "price_earning = pd.read_csv('F:/Python2025/python/datasets/Price_earnings_mon2024.csv')\n",
    "price_earning['month'] = pd.date_range(start='1991-01-31', end='2024-12-31', freq='ME')\n",
    "price_earning.set_index('month', inplace=True)\n",
    "price_earning.sort_index(inplace=True)\n",
    "\n",
    "price_bookvalue = pd.read_csv('F:/Python2025/python/datasets/Price_bookvalue_mon2024.csv')\n",
    "price_bookvalue['month'] = pd.date_range(start='1990-12-31', end='2024-12-31', freq='ME')\n",
    "price_bookvalue.set_index('month', inplace=True)\n",
    "price_bookvalue.sort_index(inplace=True)\n",
    "price_bookvalue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>to_v</th>\n",
       "      <th>to_m</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-12-31</th>\n",
       "      <td>0.009403</td>\n",
       "      <td>0.009754</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-01-31</th>\n",
       "      <td>0.012623</td>\n",
       "      <td>0.031899</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-02-28</th>\n",
       "      <td>0.042994</td>\n",
       "      <td>0.046496</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-03-31</th>\n",
       "      <td>0.006471</td>\n",
       "      <td>0.016755</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-04-30</th>\n",
       "      <td>0.014430</td>\n",
       "      <td>0.026691</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>0.205272</td>\n",
       "      <td>0.203924</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.235540</td>\n",
       "      <td>0.231543</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-10-31</th>\n",
       "      <td>0.424766</td>\n",
       "      <td>0.464635</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-30</th>\n",
       "      <td>0.493320</td>\n",
       "      <td>0.514568</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-31</th>\n",
       "      <td>0.454830</td>\n",
       "      <td>0.439975</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>409 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                to_v      to_m\n",
       "month                         \n",
       "1990-12-31  0.009403  0.009754\n",
       "1991-01-31  0.012623  0.031899\n",
       "1991-02-28  0.042994  0.046496\n",
       "1991-03-31  0.006471  0.016755\n",
       "1991-04-30  0.014430  0.026691\n",
       "...              ...       ...\n",
       "2024-08-31  0.205272  0.203924\n",
       "2024-09-30  0.235540  0.231543\n",
       "2024-10-31  0.424766  0.464635\n",
       "2024-11-30  0.493320  0.514568\n",
       "2024-12-31  0.454830  0.439975\n",
       "\n",
       "[409 rows x 2 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Turnover = pd.read_csv('F:/Python2025/python/datasets/Turnover_mon2024.csv')\n",
    "Turnover['month'] = pd.date_range(start='1990-12-31', periods=len(Turnover), freq='ME')\n",
    "Turnover.set_index('month', inplace=True)\n",
    "Turnover.sort_index(inplace=True)\n",
    "Turnover"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MarketR</th>\n",
       "      <th>rfmonth</th>\n",
       "      <th>ret</th>\n",
       "      <th>cpi</th>\n",
       "      <th>RV</th>\n",
       "      <th>RV1</th>\n",
       "      <th>RV2</th>\n",
       "      <th>RV3</th>\n",
       "      <th>var</th>\n",
       "      <th>pd</th>\n",
       "      <th>pe</th>\n",
       "      <th>pb</th>\n",
       "      <th>to_v</th>\n",
       "      <th>marketret3</th>\n",
       "      <th>marketret6</th>\n",
       "      <th>marketret12</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1991-01-31</th>\n",
       "      <td>0.029998</td>\n",
       "      <td>0.006930</td>\n",
       "      <td>0.023068</td>\n",
       "      <td>2.2</td>\n",
       "      <td>0.000690</td>\n",
       "      <td>0.001566</td>\n",
       "      <td>0.002593</td>\n",
       "      <td>0.003461</td>\n",
       "      <td>0.000030</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.466562</td>\n",
       "      <td>2.080065</td>\n",
       "      <td>0.012623</td>\n",
       "      <td>-0.084127</td>\n",
       "      <td>-0.305662</td>\n",
       "      <td>0.254049</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-02-28</th>\n",
       "      <td>0.010203</td>\n",
       "      <td>0.006930</td>\n",
       "      <td>0.003273</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.000418</td>\n",
       "      <td>0.000707</td>\n",
       "      <td>0.000853</td>\n",
       "      <td>0.000763</td>\n",
       "      <td>0.000024</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.501042</td>\n",
       "      <td>1.949285</td>\n",
       "      <td>0.042994</td>\n",
       "      <td>-0.183573</td>\n",
       "      <td>-0.384745</td>\n",
       "      <td>0.241492</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-03-31</th>\n",
       "      <td>-0.099663</td>\n",
       "      <td>0.006930</td>\n",
       "      <td>-0.106593</td>\n",
       "      <td>1.6</td>\n",
       "      <td>0.001229</td>\n",
       "      <td>0.002925</td>\n",
       "      <td>0.004650</td>\n",
       "      <td>0.006369</td>\n",
       "      <td>0.000014</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.112082</td>\n",
       "      <td>1.560324</td>\n",
       "      <td>0.006471</td>\n",
       "      <td>-0.252928</td>\n",
       "      <td>-0.445049</td>\n",
       "      <td>0.288857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-04-30</th>\n",
       "      <td>-0.079652</td>\n",
       "      <td>0.006651</td>\n",
       "      <td>-0.086303</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.000855</td>\n",
       "      <td>0.001973</td>\n",
       "      <td>0.003364</td>\n",
       "      <td>0.004531</td>\n",
       "      <td>0.000010</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.111121</td>\n",
       "      <td>1.970330</td>\n",
       "      <td>0.014430</td>\n",
       "      <td>-0.234776</td>\n",
       "      <td>-0.394937</td>\n",
       "      <td>0.691749</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-05-31</th>\n",
       "      <td>-0.074521</td>\n",
       "      <td>0.006092</td>\n",
       "      <td>-0.080613</td>\n",
       "      <td>3.6</td>\n",
       "      <td>0.000480</td>\n",
       "      <td>0.001262</td>\n",
       "      <td>0.002119</td>\n",
       "      <td>0.002949</td>\n",
       "      <td>0.000005</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.182871</td>\n",
       "      <td>1.901101</td>\n",
       "      <td>0.039698</td>\n",
       "      <td>-0.236294</td>\n",
       "      <td>0.181673</td>\n",
       "      <td>1.542701</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>-0.031468</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>-0.032586</td>\n",
       "      <td>0.6</td>\n",
       "      <td>0.000881</td>\n",
       "      <td>0.000823</td>\n",
       "      <td>0.000487</td>\n",
       "      <td>0.000487</td>\n",
       "      <td>0.000040</td>\n",
       "      <td>10.728048</td>\n",
       "      <td>2.502897</td>\n",
       "      <td>0.097936</td>\n",
       "      <td>0.205272</td>\n",
       "      <td>0.151050</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.195992</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>0.194874</td>\n",
       "      <td>0.4</td>\n",
       "      <td>0.012481</td>\n",
       "      <td>0.023868</td>\n",
       "      <td>0.034838</td>\n",
       "      <td>0.041347</td>\n",
       "      <td>0.000593</td>\n",
       "      <td>10.889979</td>\n",
       "      <td>2.675435</td>\n",
       "      <td>0.275764</td>\n",
       "      <td>0.235540</td>\n",
       "      <td>0.200147</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-10-31</th>\n",
       "      <td>-0.003409</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>-0.004527</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.011652</td>\n",
       "      <td>0.007954</td>\n",
       "      <td>0.006707</td>\n",
       "      <td>0.006707</td>\n",
       "      <td>0.000685</td>\n",
       "      <td>10.862945</td>\n",
       "      <td>2.635010</td>\n",
       "      <td>0.254341</td>\n",
       "      <td>0.424766</td>\n",
       "      <td>0.000228</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-30</th>\n",
       "      <td>0.009724</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>0.008606</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.004019</td>\n",
       "      <td>0.004118</td>\n",
       "      <td>0.005938</td>\n",
       "      <td>0.003775</td>\n",
       "      <td>0.000201</td>\n",
       "      <td>10.858076</td>\n",
       "      <td>2.643930</td>\n",
       "      <td>0.263924</td>\n",
       "      <td>0.493320</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-31</th>\n",
       "      <td>-0.002679</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>-0.003797</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.001713</td>\n",
       "      <td>0.001517</td>\n",
       "      <td>0.001623</td>\n",
       "      <td>0.001167</td>\n",
       "      <td>0.000082</td>\n",
       "      <td>10.842070</td>\n",
       "      <td>2.652927</td>\n",
       "      <td>0.261665</td>\n",
       "      <td>0.454830</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>408 rows × 16 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             MarketR   rfmonth       ret  cpi        RV       RV1       RV2  \\\n",
       "month                                                                         \n",
       "1991-01-31  0.029998  0.006930  0.023068  2.2  0.000690  0.001566  0.002593   \n",
       "1991-02-28  0.010203  0.006930  0.003273  1.0  0.000418  0.000707  0.000853   \n",
       "1991-03-31 -0.099663  0.006930 -0.106593  1.6  0.001229  0.002925  0.004650   \n",
       "1991-04-30 -0.079652  0.006651 -0.086303  1.3  0.000855  0.001973  0.003364   \n",
       "1991-05-31 -0.074521  0.006092 -0.080613  3.6  0.000480  0.001262  0.002119   \n",
       "...              ...       ...       ...  ...       ...       ...       ...   \n",
       "2024-08-31 -0.031468  0.001118 -0.032586  0.6  0.000881  0.000823  0.000487   \n",
       "2024-09-30  0.195992  0.001118  0.194874  0.4  0.012481  0.023868  0.034838   \n",
       "2024-10-31 -0.003409  0.001118 -0.004527  0.3  0.011652  0.007954  0.006707   \n",
       "2024-11-30  0.009724  0.001118  0.008606  0.2  0.004019  0.004118  0.005938   \n",
       "2024-12-31 -0.002679  0.001118 -0.003797  0.1  0.001713  0.001517  0.001623   \n",
       "\n",
       "                 RV3       var         pd        pe        pb      to_v  \\\n",
       "month                                                                     \n",
       "1991-01-31  0.003461  0.000030        NaN  4.466562  2.080065  0.012623   \n",
       "1991-02-28  0.000763  0.000024        NaN  4.501042  1.949285  0.042994   \n",
       "1991-03-31  0.006369  0.000014        NaN  4.112082  1.560324  0.006471   \n",
       "1991-04-30  0.004531  0.000010        NaN  4.111121  1.970330  0.014430   \n",
       "1991-05-31  0.002949  0.000005        NaN  4.182871  1.901101  0.039698   \n",
       "...              ...       ...        ...       ...       ...       ...   \n",
       "2024-08-31  0.000487  0.000040  10.728048  2.502897  0.097936  0.205272   \n",
       "2024-09-30  0.041347  0.000593  10.889979  2.675435  0.275764  0.235540   \n",
       "2024-10-31  0.006707  0.000685  10.862945  2.635010  0.254341  0.424766   \n",
       "2024-11-30  0.003775  0.000201  10.858076  2.643930  0.263924  0.493320   \n",
       "2024-12-31  0.001167  0.000082  10.842070  2.652927  0.261665  0.454830   \n",
       "\n",
       "            marketret3  marketret6  marketret12  \n",
       "month                                            \n",
       "1991-01-31   -0.084127   -0.305662     0.254049  \n",
       "1991-02-28   -0.183573   -0.384745     0.241492  \n",
       "1991-03-31   -0.252928   -0.445049     0.288857  \n",
       "1991-04-30   -0.234776   -0.394937     0.691749  \n",
       "1991-05-31   -0.236294    0.181673     1.542701  \n",
       "...                ...         ...          ...  \n",
       "2024-08-31    0.151050         NaN          NaN  \n",
       "2024-09-30    0.200147         NaN          NaN  \n",
       "2024-10-31    0.000228         NaN          NaN  \n",
       "2024-11-30         NaN         NaN          NaN  \n",
       "2024-12-31         NaN         NaN          NaN  \n",
       "\n",
       "[408 rows x 16 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 合并所有数据\n",
    "reg_data = pd.merge(Market_ret,inflation,on = 'month')\n",
    "reg_data = pd.merge(reg_data,Market_variance,on = 'month')\n",
    "reg_data = pd.merge(reg_data,price_dividend,on = 'month')\n",
    "reg_data = pd.merge(reg_data,price_earning,on = 'month')\n",
    "reg_data = pd.merge(reg_data,price_bookvalue,on = 'month')\n",
    "reg_data = pd.merge(reg_data,Turnover,on = 'month')\n",
    "\n",
    "reg_data = reg_data[['MarketR','rfmonth','ret','cpi','RV','RV1','RV2','RV3','var','pd','pe','pb','to_v','marketret3','marketret6','marketret12']]\n",
    "reg_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MarketR</th>\n",
       "      <th>rfmonth</th>\n",
       "      <th>ret</th>\n",
       "      <th>cpi</th>\n",
       "      <th>RV</th>\n",
       "      <th>RV1</th>\n",
       "      <th>RV2</th>\n",
       "      <th>RV3</th>\n",
       "      <th>var</th>\n",
       "      <th>pd</th>\n",
       "      <th>pe</th>\n",
       "      <th>pb</th>\n",
       "      <th>to_v</th>\n",
       "      <th>marketret3</th>\n",
       "      <th>marketret6</th>\n",
       "      <th>marketret12</th>\n",
       "      <th>lRV</th>\n",
       "      <th>lRV1</th>\n",
       "      <th>lRV2</th>\n",
       "      <th>lRV3</th>\n",
       "      <th>lcpi</th>\n",
       "      <th>lpd</th>\n",
       "      <th>lpe</th>\n",
       "      <th>lpb</th>\n",
       "      <th>lto_v</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1991-01-31</th>\n",
       "      <td>0.029998</td>\n",
       "      <td>0.006930</td>\n",
       "      <td>0.023068</td>\n",
       "      <td>2.2</td>\n",
       "      <td>0.000690</td>\n",
       "      <td>0.001566</td>\n",
       "      <td>0.002593</td>\n",
       "      <td>0.003461</td>\n",
       "      <td>0.000030</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.466562</td>\n",
       "      <td>2.080065</td>\n",
       "      <td>0.012623</td>\n",
       "      <td>-0.084127</td>\n",
       "      <td>-0.305662</td>\n",
       "      <td>0.254049</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-02-28</th>\n",
       "      <td>0.010203</td>\n",
       "      <td>0.006930</td>\n",
       "      <td>0.003273</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.000418</td>\n",
       "      <td>0.000707</td>\n",
       "      <td>0.000853</td>\n",
       "      <td>0.000763</td>\n",
       "      <td>0.000024</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.501042</td>\n",
       "      <td>1.949285</td>\n",
       "      <td>0.042994</td>\n",
       "      <td>-0.183573</td>\n",
       "      <td>-0.384745</td>\n",
       "      <td>0.241492</td>\n",
       "      <td>0.000690</td>\n",
       "      <td>0.001566</td>\n",
       "      <td>0.002593</td>\n",
       "      <td>0.003461</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.466562</td>\n",
       "      <td>2.080065</td>\n",
       "      <td>0.012623</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-03-31</th>\n",
       "      <td>-0.099663</td>\n",
       "      <td>0.006930</td>\n",
       "      <td>-0.106593</td>\n",
       "      <td>1.6</td>\n",
       "      <td>0.001229</td>\n",
       "      <td>0.002925</td>\n",
       "      <td>0.004650</td>\n",
       "      <td>0.006369</td>\n",
       "      <td>0.000014</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.112082</td>\n",
       "      <td>1.560324</td>\n",
       "      <td>0.006471</td>\n",
       "      <td>-0.252928</td>\n",
       "      <td>-0.445049</td>\n",
       "      <td>0.288857</td>\n",
       "      <td>0.000418</td>\n",
       "      <td>0.000707</td>\n",
       "      <td>0.000853</td>\n",
       "      <td>0.000763</td>\n",
       "      <td>2.2</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.501042</td>\n",
       "      <td>1.949285</td>\n",
       "      <td>0.042994</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-04-30</th>\n",
       "      <td>-0.079652</td>\n",
       "      <td>0.006651</td>\n",
       "      <td>-0.086303</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.000855</td>\n",
       "      <td>0.001973</td>\n",
       "      <td>0.003364</td>\n",
       "      <td>0.004531</td>\n",
       "      <td>0.000010</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.111121</td>\n",
       "      <td>1.970330</td>\n",
       "      <td>0.014430</td>\n",
       "      <td>-0.234776</td>\n",
       "      <td>-0.394937</td>\n",
       "      <td>0.691749</td>\n",
       "      <td>0.001229</td>\n",
       "      <td>0.002925</td>\n",
       "      <td>0.004650</td>\n",
       "      <td>0.006369</td>\n",
       "      <td>1.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.112082</td>\n",
       "      <td>1.560324</td>\n",
       "      <td>0.006471</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1991-05-31</th>\n",
       "      <td>-0.074521</td>\n",
       "      <td>0.006092</td>\n",
       "      <td>-0.080613</td>\n",
       "      <td>3.6</td>\n",
       "      <td>0.000480</td>\n",
       "      <td>0.001262</td>\n",
       "      <td>0.002119</td>\n",
       "      <td>0.002949</td>\n",
       "      <td>0.000005</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.182871</td>\n",
       "      <td>1.901101</td>\n",
       "      <td>0.039698</td>\n",
       "      <td>-0.236294</td>\n",
       "      <td>0.181673</td>\n",
       "      <td>1.542701</td>\n",
       "      <td>0.000855</td>\n",
       "      <td>0.001973</td>\n",
       "      <td>0.003364</td>\n",
       "      <td>0.004531</td>\n",
       "      <td>1.6</td>\n",
       "      <td>NaN</td>\n",
       "      <td>4.111121</td>\n",
       "      <td>1.970330</td>\n",
       "      <td>0.014430</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>-0.031468</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>-0.032586</td>\n",
       "      <td>0.6</td>\n",
       "      <td>0.000881</td>\n",
       "      <td>0.000823</td>\n",
       "      <td>0.000487</td>\n",
       "      <td>0.000487</td>\n",
       "      <td>0.000040</td>\n",
       "      <td>10.728048</td>\n",
       "      <td>2.502897</td>\n",
       "      <td>0.097936</td>\n",
       "      <td>0.205272</td>\n",
       "      <td>0.151050</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.001878</td>\n",
       "      <td>0.001692</td>\n",
       "      <td>0.002073</td>\n",
       "      <td>0.001693</td>\n",
       "      <td>0.2</td>\n",
       "      <td>10.778043</td>\n",
       "      <td>2.544499</td>\n",
       "      <td>0.127471</td>\n",
       "      <td>0.211110</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.195992</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>0.194874</td>\n",
       "      <td>0.4</td>\n",
       "      <td>0.012481</td>\n",
       "      <td>0.023868</td>\n",
       "      <td>0.034838</td>\n",
       "      <td>0.041347</td>\n",
       "      <td>0.000593</td>\n",
       "      <td>10.889979</td>\n",
       "      <td>2.675435</td>\n",
       "      <td>0.275764</td>\n",
       "      <td>0.235540</td>\n",
       "      <td>0.200147</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.000881</td>\n",
       "      <td>0.000823</td>\n",
       "      <td>0.000487</td>\n",
       "      <td>0.000487</td>\n",
       "      <td>0.5</td>\n",
       "      <td>10.728048</td>\n",
       "      <td>2.502897</td>\n",
       "      <td>0.097936</td>\n",
       "      <td>0.205272</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-10-31</th>\n",
       "      <td>-0.003409</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>-0.004527</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.011652</td>\n",
       "      <td>0.007954</td>\n",
       "      <td>0.006707</td>\n",
       "      <td>0.006707</td>\n",
       "      <td>0.000685</td>\n",
       "      <td>10.862945</td>\n",
       "      <td>2.635010</td>\n",
       "      <td>0.254341</td>\n",
       "      <td>0.424766</td>\n",
       "      <td>0.000228</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.012481</td>\n",
       "      <td>0.023868</td>\n",
       "      <td>0.034838</td>\n",
       "      <td>0.041347</td>\n",
       "      <td>0.6</td>\n",
       "      <td>10.889979</td>\n",
       "      <td>2.675435</td>\n",
       "      <td>0.275764</td>\n",
       "      <td>0.235540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-30</th>\n",
       "      <td>0.009724</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>0.008606</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.004019</td>\n",
       "      <td>0.004118</td>\n",
       "      <td>0.005938</td>\n",
       "      <td>0.003775</td>\n",
       "      <td>0.000201</td>\n",
       "      <td>10.858076</td>\n",
       "      <td>2.643930</td>\n",
       "      <td>0.263924</td>\n",
       "      <td>0.493320</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.011652</td>\n",
       "      <td>0.007954</td>\n",
       "      <td>0.006707</td>\n",
       "      <td>0.006707</td>\n",
       "      <td>0.4</td>\n",
       "      <td>10.862945</td>\n",
       "      <td>2.635010</td>\n",
       "      <td>0.254341</td>\n",
       "      <td>0.424766</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-31</th>\n",
       "      <td>-0.002679</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>-0.003797</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.001713</td>\n",
       "      <td>0.001517</td>\n",
       "      <td>0.001623</td>\n",
       "      <td>0.001167</td>\n",
       "      <td>0.000082</td>\n",
       "      <td>10.842070</td>\n",
       "      <td>2.652927</td>\n",
       "      <td>0.261665</td>\n",
       "      <td>0.454830</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.004019</td>\n",
       "      <td>0.004118</td>\n",
       "      <td>0.005938</td>\n",
       "      <td>0.003775</td>\n",
       "      <td>0.3</td>\n",
       "      <td>10.858076</td>\n",
       "      <td>2.643930</td>\n",
       "      <td>0.263924</td>\n",
       "      <td>0.493320</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>408 rows × 25 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             MarketR   rfmonth       ret  cpi        RV       RV1       RV2  \\\n",
       "month                                                                         \n",
       "1991-01-31  0.029998  0.006930  0.023068  2.2  0.000690  0.001566  0.002593   \n",
       "1991-02-28  0.010203  0.006930  0.003273  1.0  0.000418  0.000707  0.000853   \n",
       "1991-03-31 -0.099663  0.006930 -0.106593  1.6  0.001229  0.002925  0.004650   \n",
       "1991-04-30 -0.079652  0.006651 -0.086303  1.3  0.000855  0.001973  0.003364   \n",
       "1991-05-31 -0.074521  0.006092 -0.080613  3.6  0.000480  0.001262  0.002119   \n",
       "...              ...       ...       ...  ...       ...       ...       ...   \n",
       "2024-08-31 -0.031468  0.001118 -0.032586  0.6  0.000881  0.000823  0.000487   \n",
       "2024-09-30  0.195992  0.001118  0.194874  0.4  0.012481  0.023868  0.034838   \n",
       "2024-10-31 -0.003409  0.001118 -0.004527  0.3  0.011652  0.007954  0.006707   \n",
       "2024-11-30  0.009724  0.001118  0.008606  0.2  0.004019  0.004118  0.005938   \n",
       "2024-12-31 -0.002679  0.001118 -0.003797  0.1  0.001713  0.001517  0.001623   \n",
       "\n",
       "                 RV3       var         pd        pe        pb      to_v  \\\n",
       "month                                                                     \n",
       "1991-01-31  0.003461  0.000030        NaN  4.466562  2.080065  0.012623   \n",
       "1991-02-28  0.000763  0.000024        NaN  4.501042  1.949285  0.042994   \n",
       "1991-03-31  0.006369  0.000014        NaN  4.112082  1.560324  0.006471   \n",
       "1991-04-30  0.004531  0.000010        NaN  4.111121  1.970330  0.014430   \n",
       "1991-05-31  0.002949  0.000005        NaN  4.182871  1.901101  0.039698   \n",
       "...              ...       ...        ...       ...       ...       ...   \n",
       "2024-08-31  0.000487  0.000040  10.728048  2.502897  0.097936  0.205272   \n",
       "2024-09-30  0.041347  0.000593  10.889979  2.675435  0.275764  0.235540   \n",
       "2024-10-31  0.006707  0.000685  10.862945  2.635010  0.254341  0.424766   \n",
       "2024-11-30  0.003775  0.000201  10.858076  2.643930  0.263924  0.493320   \n",
       "2024-12-31  0.001167  0.000082  10.842070  2.652927  0.261665  0.454830   \n",
       "\n",
       "            marketret3  marketret6  marketret12       lRV      lRV1      lRV2  \\\n",
       "month                                                                           \n",
       "1991-01-31   -0.084127   -0.305662     0.254049       NaN       NaN       NaN   \n",
       "1991-02-28   -0.183573   -0.384745     0.241492  0.000690  0.001566  0.002593   \n",
       "1991-03-31   -0.252928   -0.445049     0.288857  0.000418  0.000707  0.000853   \n",
       "1991-04-30   -0.234776   -0.394937     0.691749  0.001229  0.002925  0.004650   \n",
       "1991-05-31   -0.236294    0.181673     1.542701  0.000855  0.001973  0.003364   \n",
       "...                ...         ...          ...       ...       ...       ...   \n",
       "2024-08-31    0.151050         NaN          NaN  0.001878  0.001692  0.002073   \n",
       "2024-09-30    0.200147         NaN          NaN  0.000881  0.000823  0.000487   \n",
       "2024-10-31    0.000228         NaN          NaN  0.012481  0.023868  0.034838   \n",
       "2024-11-30         NaN         NaN          NaN  0.011652  0.007954  0.006707   \n",
       "2024-12-31         NaN         NaN          NaN  0.004019  0.004118  0.005938   \n",
       "\n",
       "                lRV3  lcpi        lpd       lpe       lpb     lto_v  \n",
       "month                                                                \n",
       "1991-01-31       NaN   NaN        NaN       NaN       NaN       NaN  \n",
       "1991-02-28  0.003461   NaN        NaN  4.466562  2.080065  0.012623  \n",
       "1991-03-31  0.000763   2.2        NaN  4.501042  1.949285  0.042994  \n",
       "1991-04-30  0.006369   1.0        NaN  4.112082  1.560324  0.006471  \n",
       "1991-05-31  0.004531   1.6        NaN  4.111121  1.970330  0.014430  \n",
       "...              ...   ...        ...       ...       ...       ...  \n",
       "2024-08-31  0.001693   0.2  10.778043  2.544499  0.127471  0.211110  \n",
       "2024-09-30  0.000487   0.5  10.728048  2.502897  0.097936  0.205272  \n",
       "2024-10-31  0.041347   0.6  10.889979  2.675435  0.275764  0.235540  \n",
       "2024-11-30  0.006707   0.4  10.862945  2.635010  0.254341  0.424766  \n",
       "2024-12-31  0.003775   0.3  10.858076  2.643930  0.263924  0.493320  \n",
       "\n",
       "[408 rows x 25 columns]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 创建滞后变量\n",
    "reg_data['lRV'] = reg_data['RV'].shift(1)\n",
    "reg_data['lRV1'] = reg_data['RV1'].shift(1)\n",
    "reg_data['lRV2'] = reg_data['RV2'].shift(1)\n",
    "reg_data['lRV3'] = reg_data['RV3'].shift(1)\n",
    "reg_data['lcpi'] = reg_data['cpi'].shift(2)\n",
    "reg_data['lpd'] = reg_data['pd'].shift(1)\n",
    "reg_data['lpe'] = reg_data['pe'].shift(1)\n",
    "reg_data['lpb'] = reg_data['pb'].shift(1)\n",
    "reg_data['lto_v'] = reg_data['to_v'].shift(1)\n",
    "reg_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "样本外预测"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MarketR</th>\n",
       "      <th>rfmonth</th>\n",
       "      <th>ret</th>\n",
       "      <th>cpi</th>\n",
       "      <th>RV</th>\n",
       "      <th>RV1</th>\n",
       "      <th>RV2</th>\n",
       "      <th>RV3</th>\n",
       "      <th>var</th>\n",
       "      <th>pd</th>\n",
       "      <th>pe</th>\n",
       "      <th>pb</th>\n",
       "      <th>to_v</th>\n",
       "      <th>marketret3</th>\n",
       "      <th>marketret6</th>\n",
       "      <th>marketret12</th>\n",
       "      <th>lRV</th>\n",
       "      <th>lRV1</th>\n",
       "      <th>lRV2</th>\n",
       "      <th>lRV3</th>\n",
       "      <th>lcpi</th>\n",
       "      <th>lpd</th>\n",
       "      <th>lpe</th>\n",
       "      <th>lpb</th>\n",
       "      <th>lto_v</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2024-03-31</th>\n",
       "      <td>0.016715</td>\n",
       "      <td>0.001200</td>\n",
       "      <td>0.015515</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.001174</td>\n",
       "      <td>0.001450</td>\n",
       "      <td>0.000916</td>\n",
       "      <td>0.001054</td>\n",
       "      <td>0.000058</td>\n",
       "      <td>10.831573</td>\n",
       "      <td>2.559242</td>\n",
       "      <td>0.195646</td>\n",
       "      <td>0.269898</td>\n",
       "      <td>0.022495</td>\n",
       "      <td>-0.052033</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.004431</td>\n",
       "      <td>0.005019</td>\n",
       "      <td>0.007816</td>\n",
       "      <td>0.009602</td>\n",
       "      <td>-0.8</td>\n",
       "      <td>10.813148</td>\n",
       "      <td>2.537486</td>\n",
       "      <td>0.189807</td>\n",
       "      <td>0.216073</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-04-30</th>\n",
       "      <td>0.016724</td>\n",
       "      <td>0.001200</td>\n",
       "      <td>0.015524</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.002223</td>\n",
       "      <td>0.001160</td>\n",
       "      <td>0.002283</td>\n",
       "      <td>0.000480</td>\n",
       "      <td>0.000116</td>\n",
       "      <td>10.837655</td>\n",
       "      <td>2.605339</td>\n",
       "      <td>0.189505</td>\n",
       "      <td>0.252094</td>\n",
       "      <td>-0.034238</td>\n",
       "      <td>0.116460</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.001174</td>\n",
       "      <td>0.001450</td>\n",
       "      <td>0.000916</td>\n",
       "      <td>0.001054</td>\n",
       "      <td>0.7</td>\n",
       "      <td>10.831573</td>\n",
       "      <td>2.559242</td>\n",
       "      <td>0.195646</td>\n",
       "      <td>0.269898</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-05-31</th>\n",
       "      <td>-0.007371</td>\n",
       "      <td>0.001200</td>\n",
       "      <td>-0.008571</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.001086</td>\n",
       "      <td>0.000785</td>\n",
       "      <td>0.000768</td>\n",
       "      <td>0.001512</td>\n",
       "      <td>0.000057</td>\n",
       "      <td>10.838736</td>\n",
       "      <td>2.599313</td>\n",
       "      <td>0.182497</td>\n",
       "      <td>0.230006</td>\n",
       "      <td>-0.049633</td>\n",
       "      <td>0.094295</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.002223</td>\n",
       "      <td>0.001160</td>\n",
       "      <td>0.002283</td>\n",
       "      <td>0.000480</td>\n",
       "      <td>0.1</td>\n",
       "      <td>10.837655</td>\n",
       "      <td>2.605339</td>\n",
       "      <td>0.189505</td>\n",
       "      <td>0.252094</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>-0.039499</td>\n",
       "      <td>0.001200</td>\n",
       "      <td>-0.040699</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.000934</td>\n",
       "      <td>0.000445</td>\n",
       "      <td>0.000867</td>\n",
       "      <td>0.001179</td>\n",
       "      <td>0.000047</td>\n",
       "      <td>10.770461</td>\n",
       "      <td>2.557868</td>\n",
       "      <td>0.136221</td>\n",
       "      <td>0.184419</td>\n",
       "      <td>-0.072709</td>\n",
       "      <td>0.113343</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.001086</td>\n",
       "      <td>0.000785</td>\n",
       "      <td>0.000768</td>\n",
       "      <td>0.001512</td>\n",
       "      <td>0.3</td>\n",
       "      <td>10.838736</td>\n",
       "      <td>2.599313</td>\n",
       "      <td>0.182497</td>\n",
       "      <td>0.230006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-07-31</th>\n",
       "      <td>0.000560</td>\n",
       "      <td>0.001184</td>\n",
       "      <td>-0.000624</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.001878</td>\n",
       "      <td>0.001692</td>\n",
       "      <td>0.002073</td>\n",
       "      <td>0.001693</td>\n",
       "      <td>0.000085</td>\n",
       "      <td>10.778043</td>\n",
       "      <td>2.544499</td>\n",
       "      <td>0.127471</td>\n",
       "      <td>0.211110</td>\n",
       "      <td>0.155581</td>\n",
       "      <td>0.156368</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.000934</td>\n",
       "      <td>0.000445</td>\n",
       "      <td>0.000867</td>\n",
       "      <td>0.001179</td>\n",
       "      <td>0.3</td>\n",
       "      <td>10.770461</td>\n",
       "      <td>2.557868</td>\n",
       "      <td>0.136221</td>\n",
       "      <td>0.184419</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>-0.031468</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>-0.032586</td>\n",
       "      <td>0.6</td>\n",
       "      <td>0.000881</td>\n",
       "      <td>0.000823</td>\n",
       "      <td>0.000487</td>\n",
       "      <td>0.000487</td>\n",
       "      <td>0.000040</td>\n",
       "      <td>10.728048</td>\n",
       "      <td>2.502897</td>\n",
       "      <td>0.097936</td>\n",
       "      <td>0.205272</td>\n",
       "      <td>0.151050</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.001878</td>\n",
       "      <td>0.001692</td>\n",
       "      <td>0.002073</td>\n",
       "      <td>0.001693</td>\n",
       "      <td>0.2</td>\n",
       "      <td>10.778043</td>\n",
       "      <td>2.544499</td>\n",
       "      <td>0.127471</td>\n",
       "      <td>0.211110</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.195992</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>0.194874</td>\n",
       "      <td>0.4</td>\n",
       "      <td>0.012481</td>\n",
       "      <td>0.023868</td>\n",
       "      <td>0.034838</td>\n",
       "      <td>0.041347</td>\n",
       "      <td>0.000593</td>\n",
       "      <td>10.889979</td>\n",
       "      <td>2.675435</td>\n",
       "      <td>0.275764</td>\n",
       "      <td>0.235540</td>\n",
       "      <td>0.200147</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.000881</td>\n",
       "      <td>0.000823</td>\n",
       "      <td>0.000487</td>\n",
       "      <td>0.000487</td>\n",
       "      <td>0.5</td>\n",
       "      <td>10.728048</td>\n",
       "      <td>2.502897</td>\n",
       "      <td>0.097936</td>\n",
       "      <td>0.205272</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-10-31</th>\n",
       "      <td>-0.003409</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>-0.004527</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.011652</td>\n",
       "      <td>0.007954</td>\n",
       "      <td>0.006707</td>\n",
       "      <td>0.006707</td>\n",
       "      <td>0.000685</td>\n",
       "      <td>10.862945</td>\n",
       "      <td>2.635010</td>\n",
       "      <td>0.254341</td>\n",
       "      <td>0.424766</td>\n",
       "      <td>0.000228</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.012481</td>\n",
       "      <td>0.023868</td>\n",
       "      <td>0.034838</td>\n",
       "      <td>0.041347</td>\n",
       "      <td>0.6</td>\n",
       "      <td>10.889979</td>\n",
       "      <td>2.675435</td>\n",
       "      <td>0.275764</td>\n",
       "      <td>0.235540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-30</th>\n",
       "      <td>0.009724</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>0.008606</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.004019</td>\n",
       "      <td>0.004118</td>\n",
       "      <td>0.005938</td>\n",
       "      <td>0.003775</td>\n",
       "      <td>0.000201</td>\n",
       "      <td>10.858076</td>\n",
       "      <td>2.643930</td>\n",
       "      <td>0.263924</td>\n",
       "      <td>0.493320</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.011652</td>\n",
       "      <td>0.007954</td>\n",
       "      <td>0.006707</td>\n",
       "      <td>0.006707</td>\n",
       "      <td>0.4</td>\n",
       "      <td>10.862945</td>\n",
       "      <td>2.635010</td>\n",
       "      <td>0.254341</td>\n",
       "      <td>0.424766</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-31</th>\n",
       "      <td>-0.002679</td>\n",
       "      <td>0.001118</td>\n",
       "      <td>-0.003797</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.001713</td>\n",
       "      <td>0.001517</td>\n",
       "      <td>0.001623</td>\n",
       "      <td>0.001167</td>\n",
       "      <td>0.000082</td>\n",
       "      <td>10.842070</td>\n",
       "      <td>2.652927</td>\n",
       "      <td>0.261665</td>\n",
       "      <td>0.454830</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.004019</td>\n",
       "      <td>0.004118</td>\n",
       "      <td>0.005938</td>\n",
       "      <td>0.003775</td>\n",
       "      <td>0.3</td>\n",
       "      <td>10.858076</td>\n",
       "      <td>2.643930</td>\n",
       "      <td>0.263924</td>\n",
       "      <td>0.493320</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             MarketR   rfmonth       ret  cpi        RV       RV1       RV2  \\\n",
       "month                                                                         \n",
       "2024-03-31  0.016715  0.001200  0.015515  0.1  0.001174  0.001450  0.000916   \n",
       "2024-04-30  0.016724  0.001200  0.015524  0.3  0.002223  0.001160  0.002283   \n",
       "2024-05-31 -0.007371  0.001200 -0.008571  0.3  0.001086  0.000785  0.000768   \n",
       "2024-06-30 -0.039499  0.001200 -0.040699  0.2  0.000934  0.000445  0.000867   \n",
       "2024-07-31  0.000560  0.001184 -0.000624  0.5  0.001878  0.001692  0.002073   \n",
       "2024-08-31 -0.031468  0.001118 -0.032586  0.6  0.000881  0.000823  0.000487   \n",
       "2024-09-30  0.195992  0.001118  0.194874  0.4  0.012481  0.023868  0.034838   \n",
       "2024-10-31 -0.003409  0.001118 -0.004527  0.3  0.011652  0.007954  0.006707   \n",
       "2024-11-30  0.009724  0.001118  0.008606  0.2  0.004019  0.004118  0.005938   \n",
       "2024-12-31 -0.002679  0.001118 -0.003797  0.1  0.001713  0.001517  0.001623   \n",
       "\n",
       "                 RV3       var         pd        pe        pb      to_v  \\\n",
       "month                                                                     \n",
       "2024-03-31  0.001054  0.000058  10.831573  2.559242  0.195646  0.269898   \n",
       "2024-04-30  0.000480  0.000116  10.837655  2.605339  0.189505  0.252094   \n",
       "2024-05-31  0.001512  0.000057  10.838736  2.599313  0.182497  0.230006   \n",
       "2024-06-30  0.001179  0.000047  10.770461  2.557868  0.136221  0.184419   \n",
       "2024-07-31  0.001693  0.000085  10.778043  2.544499  0.127471  0.211110   \n",
       "2024-08-31  0.000487  0.000040  10.728048  2.502897  0.097936  0.205272   \n",
       "2024-09-30  0.041347  0.000593  10.889979  2.675435  0.275764  0.235540   \n",
       "2024-10-31  0.006707  0.000685  10.862945  2.635010  0.254341  0.424766   \n",
       "2024-11-30  0.003775  0.000201  10.858076  2.643930  0.263924  0.493320   \n",
       "2024-12-31  0.001167  0.000082  10.842070  2.652927  0.261665  0.454830   \n",
       "\n",
       "            marketret3  marketret6  marketret12       lRV      lRV1      lRV2  \\\n",
       "month                                                                           \n",
       "2024-03-31    0.022495   -0.052033          NaN  0.004431  0.005019  0.007816   \n",
       "2024-04-30   -0.034238    0.116460          NaN  0.001174  0.001450  0.000916   \n",
       "2024-05-31   -0.049633    0.094295          NaN  0.002223  0.001160  0.002283   \n",
       "2024-06-30   -0.072709    0.113343          NaN  0.001086  0.000785  0.000768   \n",
       "2024-07-31    0.155581    0.156368          NaN  0.000934  0.000445  0.000867   \n",
       "2024-08-31    0.151050         NaN          NaN  0.001878  0.001692  0.002073   \n",
       "2024-09-30    0.200147         NaN          NaN  0.000881  0.000823  0.000487   \n",
       "2024-10-31    0.000228         NaN          NaN  0.012481  0.023868  0.034838   \n",
       "2024-11-30         NaN         NaN          NaN  0.011652  0.007954  0.006707   \n",
       "2024-12-31         NaN         NaN          NaN  0.004019  0.004118  0.005938   \n",
       "\n",
       "                lRV3  lcpi        lpd       lpe       lpb     lto_v  \n",
       "month                                                                \n",
       "2024-03-31  0.009602  -0.8  10.813148  2.537486  0.189807  0.216073  \n",
       "2024-04-30  0.001054   0.7  10.831573  2.559242  0.195646  0.269898  \n",
       "2024-05-31  0.000480   0.1  10.837655  2.605339  0.189505  0.252094  \n",
       "2024-06-30  0.001512   0.3  10.838736  2.599313  0.182497  0.230006  \n",
       "2024-07-31  0.001179   0.3  10.770461  2.557868  0.136221  0.184419  \n",
       "2024-08-31  0.001693   0.2  10.778043  2.544499  0.127471  0.211110  \n",
       "2024-09-30  0.000487   0.5  10.728048  2.502897  0.097936  0.205272  \n",
       "2024-10-31  0.041347   0.6  10.889979  2.675435  0.275764  0.235540  \n",
       "2024-11-30  0.006707   0.4  10.862945  2.635010  0.254341  0.424766  \n",
       "2024-12-31  0.003775   0.3  10.858076  2.643930  0.263924  0.493320  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 查看数据\n",
    "reg_data.tail(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "使用已实现波动率(RV3)的样本外R²是: -0.0693\n"
     ]
    }
   ],
   "source": [
    "data = reg_data['2000-01':'2024-12'].copy()\n",
    "data = data.dropna()  # 删除缺失值\n",
    "\n",
    "# 初始化误差累加器\n",
    "total_model_error = 0.0\n",
    "total_benchmark_error = 0.0\n",
    "\n",
    "# 确定滚动窗口的起始点\n",
    "initial_train_size = int(len(data) / 3)\n",
    "\n",
    "# 滚动窗口预测循环\n",
    "for i in range(initial_train_size, len(data) - 1):\n",
    "    # 划分训练集和测试集\n",
    "    train_data = data.iloc[:i]\n",
    "    test_data = data.iloc[i:i+1]\n",
    "    \n",
    "    # 训练OLS模型\n",
    "    model = smf.ols(formula='ret ~ lRV3', data=train_data).fit(disp=False)\n",
    "    \n",
    "    # 进行预测并计算实际值\n",
    "    model_pred = model.predict(test_data[['lRV3']]).iloc[0]\n",
    "    benchmark_pred = train_data['ret'].mean()\n",
    "    actual_ret = test_data['ret'].iloc[0]\n",
    "    \n",
    "    # 累加平方误差\n",
    "    total_model_error += (model_pred - actual_ret) ** 2\n",
    "    total_benchmark_error += (benchmark_pred - actual_ret) ** 2\n",
    "\n",
    "# 5计算并打印样本外R²\n",
    "oos_r2 = 1 - (total_model_error / total_benchmark_error)\n",
    "print(f\"使用已实现波动率(RV3)的样本外R²是: {oos_r2:.4f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "单变量模型:\n",
      "RV3模型: [-0.08398473]\n",
      "CPI模型: [-0.02056036]\n",
      "PD模型: [-0.00564408]\n",
      "\n",
      "多变量模型:\n",
      "RV3+CPI: [-0.15904403]\n",
      "RV3+PD: [-0.08972757]\n",
      "RV3+CPI+PD: [-0.18643754]\n"
     ]
    }
   ],
   "source": [
    "# 通用样本外预测函数 (简化版)\n",
    "data = reg_data['2000-01':'2024-12'].copy()\n",
    "data = data.dropna()  # 删除缺失值\n",
    "\n",
    "def out_of_sample_simple(data,y,x,initial_sample_fractions):\n",
    "    model_pre = 0\n",
    "    mean_pre = 0\n",
    "\n",
    "    initial_sample = int(len(data)*initial_sample_fractions)\n",
    "\n",
    "    # 模型\n",
    "    predictor_formula = \"+\".join(x)\n",
    "    formula = f'{y} ~ {predictor_formula}'\n",
    "\n",
    "    for i in range(initial_sample, len(data) - 1):\n",
    "        # 选择数据\n",
    "        data_reg = data[0:i]\n",
    "        model =smf.ols(formula, data=data_reg).fit(displ=False)\n",
    "        r_a = (model.predict(data[i:i+1][x]) - data[i:i+1][y])**2\n",
    "        r_b = (np.mean(data_reg[y]) - data[i:i+1][y])**2\n",
    "        r_a = r_a.values\n",
    "        r_b = r_b.values\n",
    "        model_pre = model_pre + r_a\n",
    "        mean_pre = mean_pre + r_b\n",
    "\n",
    "    oos = 1 - model_pre/mean_pre\n",
    "    return oos\n",
    "\n",
    "# 测试不同预测变量\n",
    "print(\"单变量模型:\")\n",
    "print(\"RV3模型:\", out_of_sample_simple(data,'ret',['lRV3'],0.5))\n",
    "print(\"CPI模型:\", out_of_sample_simple(data,'ret',['lcpi'],0.5))\n",
    "print(\"PD模型:\", out_of_sample_simple(data,'ret',['lpd'],0.5))\n",
    "print(\"\\n多变量模型:\")\n",
    "print(\"RV3+CPI:\", out_of_sample_simple(data,'ret',['lRV3','lcpi'],0.5))\n",
    "print(\"RV3+PD:\", out_of_sample_simple(data,'ret',['lRV3','lpd'],0.5))\n",
    "print(\"RV3+CPI+PD:\", out_of_sample_simple(data,'ret',['lRV3','lcpi','lpd'],0.5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "初始样本比例对样本外R2的影响:\n",
      "初始样本比例 0.1: OOS R2 = -0.033798\n",
      "初始样本比例 0.2: OOS R2 = 0.003662\n",
      "初始样本比例 0.3: OOS R2 = 0.008066\n",
      "初始样本比例 0.4: OOS R2 = -0.171586\n",
      "初始样本比例 0.5: OOS R2 = -0.186438\n",
      "初始样本比例 0.6: OOS R2 = -0.230610\n",
      "初始样本比例 0.7: OOS R2 = -0.107323\n",
      "初始样本比例 0.8: OOS R2 = -0.158921\n",
      "初始样本比例 0.9: OOS R2 = -0.183142\n"
     ]
    }
   ],
   "source": [
    "# 测试不同初始样本比例的影响\n",
    "sample_fractions = np.linspace(0.1,0.9,9)\n",
    "\n",
    "results = {}\n",
    "\n",
    "for i in sample_fractions:\n",
    "    results[i] = out_of_sample_simple(data,'ret',['lRV3','lcpi','lpd'],i)\n",
    "\n",
    "# 打印数值i\n",
    "print(\"初始样本比例对样本外R2的影响:\")\n",
    "for i, j in results.items():\n",
    "    print(f\"初始样本比例 {round(i,1)}: OOS R2 = {j[0]:.6f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "使用已实现波动率(RV3)预测:\n",
      "样本外的R方是 -0.0693\n",
      "样本外的ENC-NEW是 -2.6143\n",
      "样本外的MSE-F是 -12.5127\n"
     ]
    }
   ],
   "source": [
    "# 数据预处理（使用已有数据，无需重新生成）\n",
    "data = reg_data['2000-01':'2024-12'].copy()\n",
    "data = data.dropna()  # 删除缺失值\n",
    "\n",
    "# 初始化误差累加器\n",
    "augment = 0.0  # 模型预测误差平方和\n",
    "benchmark = 0.0  # 基准预测误差平方和\n",
    "ab = 0.0  # 模型误差与基准误差的乘积和\n",
    "\n",
    "# 确定初始训练窗口大小\n",
    "initial_train_size = int(len(data) / 3)\n",
    "\n",
    "# 滚动窗口预测与误差计算\n",
    "for i in range(initial_train_size, len(data) - 1):\n",
    "    # 划分训练集和测试集\n",
    "    train_data = data.iloc[:i]\n",
    "    test_data = data.iloc[i:i+1]\n",
    "    \n",
    "    # 训练OLS模型\n",
    "    model = smf.ols('ret ~ lRV3', data=train_data).fit(disp=False)\n",
    "    \n",
    "    # 计算预测值与实际值\n",
    "    model_pred = model.predict(test_data[['lRV3']]).iloc[0]\n",
    "    benchmark_pred = train_data['ret'].mean()\n",
    "    actual_ret = test_data['ret'].iloc[0]\n",
    "    \n",
    "    # 计算误差项并累加\n",
    "    error_model = model_pred - actual_ret\n",
    "    error_benchmark = benchmark_pred - actual_ret\n",
    "    \n",
    "    augment += error_model ** 2\n",
    "    benchmark += error_benchmark ** 2\n",
    "    ab += error_model * error_benchmark\n",
    "\n",
    "# 计算评估指标\n",
    "oos_r2 = 1 - (augment / benchmark)\n",
    "num_test_samples = len(data) - initial_train_size  # 测试样本数量\n",
    "enc_new = ((benchmark - ab) / augment) * num_test_samples\n",
    "mse_f = (benchmark - augment) / augment * num_test_samples  # 与ENC-NEW公式一致\n",
    "\n",
    "# 输出结果\n",
    "print('使用已实现波动率(RV3)预测:')\n",
    "print(f'样本外的R方是 {oos_r2:.4f}')\n",
    "print(f'样本外的ENC-NEW是 {enc_new:.4f}')\n",
    "print(f'样本外的MSE-F是 {mse_f:.4f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "使用RV3+PD预测:\n",
      "样本外的R方是 -0.0752\n",
      "样本外的ENC-NEW是 -3.0386\n",
      "样本外的MSE-F是 -13.4981\n"
     ]
    }
   ],
   "source": [
    "# 数据预处理\n",
    "data = reg_data['2000-01':'2024-12'].copy()\n",
    "data = data.dropna()\n",
    "\n",
    "# 初始化误差累加器\n",
    "augment = 0.0\n",
    "benchmark = 0.0\n",
    "ab = 0.0\n",
    "\n",
    "# 确定初始训练窗口大小\n",
    "initial_train_size = int(len(data) / 3)\n",
    "\n",
    "# 滚动窗口预测与误差计算\n",
    "for i in range(initial_train_size, len(data) - 1):\n",
    "    # 划分训练集和测试集\n",
    "    train_data = data.iloc[:i]\n",
    "    test_data = data.iloc[i:i+1]\n",
    "    \n",
    "    # 训练多变量OLS模型\n",
    "    model = smf.ols('ret ~ lRV3 + lpd', data=train_data).fit(disp=False)\n",
    "    \n",
    "    # 计算预测值与实际值\n",
    "    model_pred = model.predict(test_data[['lRV3', 'lpd']]).iloc[0]\n",
    "    benchmark_pred = train_data['ret'].mean()\n",
    "    actual_ret = test_data['ret'].iloc[0]\n",
    "    \n",
    "    # 计算误差项并累加\n",
    "    error_model = model_pred - actual_ret\n",
    "    error_benchmark = benchmark_pred - actual_ret\n",
    "    \n",
    "    augment += error_model ** 2\n",
    "    benchmark += error_benchmark ** 2\n",
    "    ab += error_model * error_benchmark\n",
    "\n",
    "# 计算评估指标\n",
    "oos_r2 = 1 - (augment / benchmark)\n",
    "num_test_samples = len(data) - initial_train_size\n",
    "enc_new = ((benchmark - ab) / augment) * num_test_samples\n",
    "mse_f = (benchmark - augment) / augment * num_test_samples\n",
    "\n",
    "# 输出结果\n",
    "print('使用RV3+PD预测:')\n",
    "print(f'样本外的R方是 {oos_r2:.4f}')\n",
    "print(f'样本外的ENC-NEW是 {enc_new:.4f}')\n",
    "print(f'样本外的MSE-F是 {mse_f:.4f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "使用RV3+PD+CPI预测:\n",
      "样本外的R方是 -0.0199\n",
      "样本外的ENC-NEW是 11.1652\n",
      "样本外的MSE-F是 -3.7710\n"
     ]
    }
   ],
   "source": [
    "# 数据预处理\n",
    "data = reg_data['2000-01':'2024-12'].copy()\n",
    "data = data.dropna()\n",
    "\n",
    "# 初始化误差累加器\n",
    "augment = 0.0\n",
    "benchmark = 0.0\n",
    "ab = 0.0\n",
    "\n",
    "# 确定初始训练窗口大小\n",
    "initial_train_size = int(len(data) / 3)\n",
    "\n",
    "# 滚动窗口预测与误差计算\n",
    "for i in range(initial_train_size, len(data) - 1):\n",
    "    # 划分训练集和测试集\n",
    "    train_data = data.iloc[:i]\n",
    "    test_data = data.iloc[i:i+1]\n",
    "    \n",
    "    # 训练多变量OLS模型\n",
    "    model = smf.ols('ret ~ lRV3 + lpd + lcpi', data=train_data).fit(disp=False)\n",
    "    \n",
    "    # 计算预测值与实际值\n",
    "    model_pred = model.predict(test_data[['lRV3', 'lpd', 'lcpi']]).iloc[0]\n",
    "    benchmark_pred = train_data['ret'].mean()\n",
    "    actual_ret = test_data['ret'].iloc[0]\n",
    "    \n",
    "    # 计算误差项并累加\n",
    "    error_model = model_pred - actual_ret\n",
    "    error_benchmark = benchmark_pred - actual_ret\n",
    "    \n",
    "    augment += error_model ** 2\n",
    "    benchmark += error_benchmark ** 2\n",
    "    ab += error_model * error_benchmark\n",
    "\n",
    "# 计算评估指标\n",
    "oos_r2 = 1 - (augment / benchmark)\n",
    "num_test_samples = len(data) - initial_train_size\n",
    "enc_new = ((benchmark - ab) / augment) * num_test_samples\n",
    "mse_f = (benchmark - augment) / augment * num_test_samples\n",
    "\n",
    "# 输出结果\n",
    "print('使用RV3+PD+CPI预测:')\n",
    "print(f'样本外的R方是 {oos_r2:.4f}')\n",
    "print(f'样本外的ENC-NEW是 {enc_new:.4f}')\n",
    "print(f'样本外的MSE-F是 {mse_f:.4f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "使用通用函数 - RV3+PD预测:\n",
      "样本外的R方是 -0.075198\n",
      "样本外的ENC-NEW是 -3.038635\n",
      "样本外的MSE-F是 -13.498102\n"
     ]
    }
   ],
   "source": [
    "# 更具有一般性的函数（包含完整统计量）\n",
    "def out_of_sample(data, response_var, predictor_vars, initial_sample_fraction):\n",
    "    # 先删除缺失值\n",
    "    data = data.dropna()\n",
    "    \n",
    "    benchmark = 0.00\n",
    "    augment = 0.00\n",
    "    ab = 0.00\n",
    "\n",
    "    # 构建模型公式\n",
    "    predictor_formula = ' + '.join(predictor_vars) # 将predictor_vars中的元素用+连接起来\n",
    "    formula = f'{response_var} ~ {predictor_formula}' # 构建公式\n",
    "\n",
    "    initial_sample_size = int(len(data) * initial_sample_fraction) # 计算初始样本的大小\n",
    "\n",
    "    for i in range(initial_sample_size, len(data) - 1):\n",
    "        data_reg = data.iloc[0:i] # 取出前i行的数据\n",
    "        model = smf.ols(formula, data_reg).fit(displ=False) # 拟合模型\n",
    "        prediction = model.predict(data.iloc[i:i + 1][predictor_vars]) # 预测值\n",
    "        actual = data.iloc[i:i + 1][response_var].values[0] # 从data中取出第i行的response_var列的值\n",
    "\n",
    "        r_a = (prediction - actual) ** 2 # 残差平方\n",
    "        r_b = (np.mean(data_reg[response_var]) - actual) ** 2 # 均值平方\n",
    "        r_ab = (prediction - actual) * (np.mean(data_reg[response_var]) - actual) # 残差乘均值\n",
    "\n",
    "        augment += r_a.values   \n",
    "        benchmark += r_b       \n",
    "        ab += r_ab.values     \n",
    "\n",
    "    oos = 1 - augment / benchmark\n",
    "    ENCNEW = ((benchmark - ab) / augment) * (len(data) - initial_sample_size)\n",
    "    MSEF = (benchmark - augment) / augment * (len(data) - initial_sample_size)\n",
    "\n",
    "    return oos[0], ENCNEW[0], MSEF[0]\n",
    "\n",
    "# 使用函数测试\n",
    "oos, ENCNEW, MSEF = out_of_sample(reg_data['2000-01':'2024-12'], 'ret', ['lRV3','lpd'], initial_sample_fraction=1/3)\n",
    "print('使用通用函数 - RV3+PD预测:')\n",
    "print(f'样本外的R方是 {oos:.6f}')\n",
    "print(f'样本外的ENC-NEW是 {ENCNEW:.6f}')\n",
    "print(f'样本外的MSE-F是 {MSEF:.6f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "不同预测变量组合和初始样本比例的样本外预测结果:\n",
      "\n",
      "================================================================================\n",
      "\n",
      "预测变量: lRV3\n",
      "--------------------------------------------------------------------------------\n",
      "初始样本比例: 0.3 | OOS R²: -0.020064 | ENC-NEW:   3.2138 | MSE-F:  -3.9928\n",
      "初始样本比例: 0.4 | OOS R²: -0.055958 | ENC-NEW:  -2.4786 | MSE-F:  -9.2207\n",
      "初始样本比例: 0.5 | OOS R²: -0.083985 | ENC-NEW:  -3.8136 | MSE-F: -11.2343\n",
      "初始样本比例: 0.6 | OOS R²: -0.108207 | ENC-NEW:  -4.3323 | MSE-F: -11.3264\n",
      "初始样本比例: 0.7 | OOS R²: 0.012960 | ENC-NEW:   0.7774 | MSE-F:   1.1423\n",
      "初始样本比例: 0.8 | OOS R²: 0.013358 | ENC-NEW:   0.5288 | MSE-F:   0.7853\n",
      "\n",
      "预测变量: lcpi\n",
      "--------------------------------------------------------------------------------\n",
      "初始样本比例: 0.3 | OOS R²: 0.027873 | ENC-NEW:   6.2479 | MSE-F:   5.8205\n",
      "初始样本比例: 0.4 | OOS R²: -0.013061 | ENC-NEW:   2.4027 | MSE-F:  -2.2434\n",
      "初始样本比例: 0.5 | OOS R²: -0.020560 | ENC-NEW:   0.1398 | MSE-F:  -2.9212\n",
      "初始样本比例: 0.6 | OOS R²: -0.030626 | ENC-NEW:  -0.4084 | MSE-F:  -3.4471\n",
      "初始样本比例: 0.7 | OOS R²: -0.084194 | ENC-NEW:  -1.2853 | MSE-F:  -6.7561\n",
      "初始样本比例: 0.8 | OOS R²: -0.132329 | ENC-NEW:  -1.4027 | MSE-F:  -6.7782\n",
      "\n",
      "预测变量: lpd\n",
      "--------------------------------------------------------------------------------\n",
      "初始样本比例: 0.3 | OOS R²: -0.005463 | ENC-NEW:  -0.3883 | MSE-F:  -1.1029\n",
      "初始样本比例: 0.4 | OOS R²: -0.009029 | ENC-NEW:  -0.5387 | MSE-F:  -1.5570\n",
      "初始样本比例: 0.5 | OOS R²: -0.005644 | ENC-NEW:  -0.2702 | MSE-F:  -0.8138\n",
      "初始样本比例: 0.6 | OOS R²: -0.001249 | ENC-NEW:   0.0237 | MSE-F:  -0.1447\n",
      "初始样本比例: 0.7 | OOS R²: -0.016333 | ENC-NEW:  -0.5929 | MSE-F:  -1.3981\n",
      "初始样本比例: 0.8 | OOS R²: -0.014366 | ENC-NEW:  -0.3460 | MSE-F:  -0.8214\n",
      "\n",
      "预测变量: lRV3+lcpi\n",
      "--------------------------------------------------------------------------------\n",
      "初始样本比例: 0.3 | OOS R²: 0.015124 | ENC-NEW:  14.6231 | MSE-F:   3.1173\n",
      "初始样本比例: 0.4 | OOS R²: -0.159989 | ENC-NEW:  -0.1337 | MSE-F: -23.9986\n",
      "初始样本比例: 0.5 | OOS R²: -0.159044 | ENC-NEW:  -4.5024 | MSE-F: -19.8969\n",
      "初始样本比例: 0.6 | OOS R²: -0.194039 | ENC-NEW:  -5.6910 | MSE-F: -18.8508\n",
      "初始样本比例: 0.7 | OOS R²: -0.058380 | ENC-NEW:  -0.3064 | MSE-F:  -4.7989\n",
      "初始样本比例: 0.8 | OOS R²: -0.107309 | ENC-NEW:  -0.8257 | MSE-F:  -5.6208\n",
      "\n",
      "预测变量: lRV3+lpd\n",
      "--------------------------------------------------------------------------------\n",
      "初始样本比例: 0.3 | OOS R²: -0.025489 | ENC-NEW:   2.6994 | MSE-F:  -5.0456\n",
      "初始样本比例: 0.4 | OOS R²: -0.063181 | ENC-NEW:  -3.0190 | MSE-F: -10.3402\n",
      "初始样本比例: 0.5 | OOS R²: -0.089728 | ENC-NEW:  -4.0561 | MSE-F: -11.9392\n",
      "初始样本比例: 0.6 | OOS R²: -0.112946 | ENC-NEW:  -4.2500 | MSE-F: -11.7721\n",
      "初始样本比例: 0.7 | OOS R²: 0.000343 | ENC-NEW:   0.1244 | MSE-F:   0.0299\n",
      "初始样本比例: 0.8 | OOS R²: 0.001867 | ENC-NEW:   0.1299 | MSE-F:   0.1085\n",
      "\n",
      "预测变量: lcpi+lpd\n",
      "--------------------------------------------------------------------------------\n",
      "初始样本比例: 0.3 | OOS R²: 0.019618 | ENC-NEW:   5.9725 | MSE-F:   4.0622\n",
      "初始样本比例: 0.4 | OOS R²: -0.025797 | ENC-NEW:   2.0242 | MSE-F:  -4.3758\n",
      "初始样本比例: 0.5 | OOS R²: -0.041133 | ENC-NEW:   0.2387 | MSE-F:  -5.7286\n",
      "初始样本比例: 0.6 | OOS R²: -0.039742 | ENC-NEW:   0.3300 | MSE-F:  -4.4339\n",
      "初始样本比例: 0.7 | OOS R²: -0.141705 | ENC-NEW:  -2.2572 | MSE-F: -10.7982\n",
      "初始样本比例: 0.8 | OOS R²: -0.188615 | ENC-NEW:  -1.9488 | MSE-F:  -9.2037\n",
      "\n",
      "预测变量: lRV3+lcpi+lpd\n",
      "--------------------------------------------------------------------------------\n",
      "初始样本比例: 0.3 | OOS R²: 0.008066 | ENC-NEW:  14.2110 | MSE-F:   1.6507\n",
      "初始样本比例: 0.4 | OOS R²: -0.171586 | ENC-NEW:  -0.7466 | MSE-F: -25.4834\n",
      "初始样本比例: 0.5 | OOS R²: -0.186438 | ENC-NEW:  -4.5302 | MSE-F: -22.7854\n",
      "初始样本比例: 0.6 | OOS R²: -0.230610 | ENC-NEW:  -5.0276 | MSE-F: -21.7378\n",
      "初始样本比例: 0.7 | OOS R²: -0.107323 | ENC-NEW:  -1.4429 | MSE-F:  -8.4321\n",
      "初始样本比例: 0.8 | OOS R²: -0.158921 | ENC-NEW:  -1.5033 | MSE-F:  -7.9535\n"
     ]
    }
   ],
   "source": [
    "# 设置不同的初始样本比例和预测变量组合\n",
    "initial_sample_fractions = [0.3, 0.4, 0.5, 0.6, 0.7,0.8]\n",
    "predictor_combinations = [\n",
    "    ['lRV3'],\n",
    "    ['lcpi'],\n",
    "    ['lpd'],\n",
    "    ['lRV3', 'lcpi'],\n",
    "    ['lRV3', 'lpd'],\n",
    "    ['lcpi', 'lpd'],\n",
    "    ['lRV3', 'lcpi', 'lpd']\n",
    "]\n",
    "\n",
    "# 用于存储结果的字典\n",
    "results = {}\n",
    "\n",
    "print(\"不同预测变量组合和初始样本比例的样本外预测结果:\\n\")\n",
    "print(\"=\"*80)\n",
    "\n",
    "for predictors in predictor_combinations:\n",
    "    predictor_name = '+'.join(predictors)\n",
    "    results[predictor_name] = {}\n",
    "    print(f\"\\n预测变量: {predictor_name}\")\n",
    "    print(\"-\"*80)\n",
    "    \n",
    "    for fraction in initial_sample_fractions:\n",
    "        # 调用 out_of_sample 函数\n",
    "        oos, ENCNEW, MSEF = out_of_sample(reg_data['2000-01':'2024-12'], 'ret', predictors, initial_sample_fraction=fraction)\n",
    "        \n",
    "        # 将结果保存到字典\n",
    "        results[predictor_name][fraction] = {\n",
    "            'OOS': oos,\n",
    "            'ENCNEW': ENCNEW,\n",
    "            'MSEF': MSEF\n",
    "        }\n",
    "        \n",
    "        # 打印结果\n",
    "        print(f\"初始样本比例: {fraction:.1f} | OOS R²: {oos:8.6f} | ENC-NEW: {ENCNEW:8.4f} | MSE-F: {MSEF:8.4f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>predicted</th>\n",
       "      <th>actual</th>\n",
       "      <th>timing_return</th>\n",
       "      <th>buy_hold_return</th>\n",
       "      <th>timing_cum</th>\n",
       "      <th>buy_hold_cum</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2012-08-31</th>\n",
       "      <td>0.004550</td>\n",
       "      <td>-0.025813</td>\n",
       "      <td>-0.025813</td>\n",
       "      <td>-0.025813</td>\n",
       "      <td>0.974187</td>\n",
       "      <td>0.974187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-09-30</th>\n",
       "      <td>-0.002805</td>\n",
       "      <td>0.021644</td>\n",
       "      <td>0.002466</td>\n",
       "      <td>0.021644</td>\n",
       "      <td>0.976589</td>\n",
       "      <td>0.995272</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-10-31</th>\n",
       "      <td>0.001722</td>\n",
       "      <td>-0.011813</td>\n",
       "      <td>-0.011813</td>\n",
       "      <td>-0.011813</td>\n",
       "      <td>0.965053</td>\n",
       "      <td>0.983515</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-11-30</th>\n",
       "      <td>0.004923</td>\n",
       "      <td>-0.062186</td>\n",
       "      <td>-0.062186</td>\n",
       "      <td>-0.062186</td>\n",
       "      <td>0.905040</td>\n",
       "      <td>0.922354</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-12-31</th>\n",
       "      <td>0.001467</td>\n",
       "      <td>0.148344</td>\n",
       "      <td>0.148344</td>\n",
       "      <td>0.148344</td>\n",
       "      <td>1.039297</td>\n",
       "      <td>1.059180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>0.005804</td>\n",
       "      <td>-0.032586</td>\n",
       "      <td>-0.032586</td>\n",
       "      <td>-0.032586</td>\n",
       "      <td>1.822628</td>\n",
       "      <td>1.568204</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.006108</td>\n",
       "      <td>0.194874</td>\n",
       "      <td>0.194874</td>\n",
       "      <td>0.194874</td>\n",
       "      <td>2.177811</td>\n",
       "      <td>1.873806</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-10-31</th>\n",
       "      <td>0.005069</td>\n",
       "      <td>-0.004527</td>\n",
       "      <td>-0.004527</td>\n",
       "      <td>-0.004527</td>\n",
       "      <td>2.167952</td>\n",
       "      <td>1.865324</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-11-30</th>\n",
       "      <td>0.035440</td>\n",
       "      <td>0.008606</td>\n",
       "      <td>0.008606</td>\n",
       "      <td>0.008606</td>\n",
       "      <td>2.186610</td>\n",
       "      <td>1.881377</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-12-31</th>\n",
       "      <td>0.010186</td>\n",
       "      <td>-0.003797</td>\n",
       "      <td>-0.003797</td>\n",
       "      <td>-0.003797</td>\n",
       "      <td>2.178307</td>\n",
       "      <td>1.874233</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>149 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            predicted    actual  timing_return  buy_hold_return  timing_cum  \\\n",
       "2012-08-31   0.004550 -0.025813      -0.025813        -0.025813    0.974187   \n",
       "2012-09-30  -0.002805  0.021644       0.002466         0.021644    0.976589   \n",
       "2012-10-31   0.001722 -0.011813      -0.011813        -0.011813    0.965053   \n",
       "2012-11-30   0.004923 -0.062186      -0.062186        -0.062186    0.905040   \n",
       "2012-12-31   0.001467  0.148344       0.148344         0.148344    1.039297   \n",
       "...               ...       ...            ...              ...         ...   \n",
       "2024-08-31   0.005804 -0.032586      -0.032586        -0.032586    1.822628   \n",
       "2024-09-30   0.006108  0.194874       0.194874         0.194874    2.177811   \n",
       "2024-10-31   0.005069 -0.004527      -0.004527        -0.004527    2.167952   \n",
       "2024-11-30   0.035440  0.008606       0.008606         0.008606    2.186610   \n",
       "2024-12-31   0.010186 -0.003797      -0.003797        -0.003797    2.178307   \n",
       "\n",
       "            buy_hold_cum  \n",
       "2012-08-31      0.974187  \n",
       "2012-09-30      0.995272  \n",
       "2012-10-31      0.983515  \n",
       "2012-11-30      0.922354  \n",
       "2012-12-31      1.059180  \n",
       "...                  ...  \n",
       "2024-08-31      1.568204  \n",
       "2024-09-30      1.873806  \n",
       "2024-10-31      1.865324  \n",
       "2024-11-30      1.881377  \n",
       "2024-12-31      1.874233  \n",
       "\n",
       "[149 rows x 6 columns]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def market_timing(data, response_var, predictor_vars, initial_sample_fraction):\n",
    "    \"\"\"\n",
    "    实现市场择时策略\n",
    "    \n",
    "    参数:\n",
    "    - data: 数据框\n",
    "    - response_var: 因变量（收益率）\n",
    "    - predictor_vars: 预测变量列表\n",
    "    - initial_sample_fraction: 初始样本比例\n",
    "    \n",
    "    返回:\n",
    "    - 包含策略表现的DataFrame\n",
    "    \"\"\"\n",
    "    # 数据预处理：删除关键变量的缺失值，保留原始索引\n",
    "    data = data.dropna(subset=[response_var] + predictor_vars).copy()\n",
    "    if len(data) == 0:\n",
    "        raise ValueError(\"数据中没有足够的非缺失值\")\n",
    "    \n",
    "    # 构建回归公式\n",
    "    formula = f'{response_var} ~ {\" + \".join(predictor_vars)}'\n",
    "    initial_sample_size = max(10, int(len(data) * initial_sample_fraction))  # 确保最小训练样本数\n",
    "    \n",
    "    # 初始化结果存储列表（预分配空间提升效率）\n",
    "    n_test = len(data) - initial_sample_size - 1\n",
    "    predictions = [0.0] * n_test\n",
    "    actual_returns = [0.0] * n_test\n",
    "    timing_returns = [0.0] * n_test\n",
    "    buy_hold_returns = [0.0] * n_test\n",
    "    dates = [pd.NaT] * n_test\n",
    "    \n",
    "    # 滚动窗口预测与策略执行\n",
    "    for i in range(n_test):\n",
    "        train_idx = slice(0, initial_sample_size + i)\n",
    "        test_idx = initial_sample_size + i\n",
    "        \n",
    "        # 训练模型\n",
    "        model = smf.ols(formula, data.iloc[train_idx]).fit(disp=False)\n",
    "        \n",
    "        # 预测下一期收益率并获取实际值\n",
    "        predicted_return = model.predict(data.iloc[[test_idx]][predictor_vars]).iloc[0]\n",
    "        actual_return = data.iloc[test_idx + 1, data.columns.get_loc(response_var)]\n",
    "        \n",
    "        # 执行择时策略（无风险利率默认0）\n",
    "        rf = data.iloc[test_idx + 1]['rfmonth'] if 'rfmonth' in data.columns else 0.0\n",
    "        timing_return = actual_return if predicted_return > 0 else rf\n",
    "        \n",
    "        # 存储结果\n",
    "        predictions[i] = predicted_return\n",
    "        actual_returns[i] = actual_return\n",
    "        timing_returns[i] = timing_return\n",
    "        buy_hold_returns[i] = actual_return\n",
    "        dates[i] = data.index[test_idx + 1]\n",
    "    \n",
    "    # 构建结果DataFrame并计算累计收益\n",
    "    results_df = pd.DataFrame({\n",
    "        'predicted': predictions,\n",
    "        'actual': actual_returns,\n",
    "        'timing_return': timing_returns,\n",
    "        'buy_hold_return': buy_hold_returns\n",
    "    }, index=dates)\n",
    "    \n",
    "    # 计算累计收益（避免复利计算错误）\n",
    "    results_df['timing_cum'] = (1 + results_df['timing_return']).cumprod()\n",
    "    results_df['buy_hold_cum'] = (1 + results_df['buy_hold_return']).cumprod()\n",
    "    \n",
    "    return results_df\n",
    "\n",
    "# 测试Market Timing策略\n",
    "timing_results = market_timing(reg_data['2000-01':'2024-12'], 'ret', ['lRV3', 'lpd'], initial_sample_fraction=1/2)\n",
    "timing_results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "============================================================\n",
      "Market Timing 策略表现\n",
      "============================================================\n",
      "Timing Cumulative Return..................... 1.1783\n",
      "Buy&Hold Cumulative Return................... 0.8742\n",
      "Timing Annualized Return..................... 0.0647\n",
      "Buy&Hold Annualized Return................... 0.0519\n",
      "Timing Volatility............................ 0.2063\n",
      "Buy&Hold Volatility.......................... 0.2131\n",
      "Timing Sharpe Ratio.......................... 0.3136\n",
      "Buy&Hold Sharpe Ratio........................ 0.2435\n",
      "Timing Max Drawdown.......................... -0.4703\n",
      "Buy&Hold Max Drawdown........................ -0.4703\n",
      "Hit Rate..................................... 0.5369\n",
      "Positive Prediction Accuracy................. 0.5396\n",
      "============================================================\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "def calculate_strategy_metrics(results_df):\n",
    "    \"\"\"计算策略表现指标\"\"\"\n",
    "    metrics = {}\n",
    "    n_years = len(results_df) / 12  # 按月度数据计算年化指标\n",
    "    timing_ret = results_df['timing_return']\n",
    "    buy_hold_ret = results_df['buy_hold_return']\n",
    "    timing_cum = results_df['timing_cum']\n",
    "    buy_hold_cum = results_df['buy_hold_cum']\n",
    "    \n",
    "    # 1. 累计收益率\n",
    "    metrics['Timing Cumulative Return'] = timing_cum.iloc[-1] - 1\n",
    "    metrics['Buy&Hold Cumulative Return'] = buy_hold_cum.iloc[-1] - 1\n",
    "    \n",
    "    # 2. 年化收益率\n",
    "    metrics['Timing Annualized Return'] = (timing_cum.iloc[-1] ** (1/n_years)) - 1\n",
    "    metrics['Buy&Hold Annualized Return'] = (buy_hold_cum.iloc[-1] ** (1/n_years)) - 1\n",
    "    \n",
    "    # 3. 年化波动率\n",
    "    metrics['Timing Volatility'] = timing_ret.std() * np.sqrt(12)\n",
    "    metrics['Buy&Hold Volatility'] = buy_hold_ret.std() * np.sqrt(12)\n",
    "    \n",
    "    # 4. 夏普比率（避免除以零）\n",
    "    metrics['Timing Sharpe Ratio'] = (metrics['Timing Annualized Return'] / metrics['Timing Volatility'] \n",
    "                                     if metrics['Timing Volatility'] != 0 else 0)\n",
    "    metrics['Buy&Hold Sharpe Ratio'] = (metrics['Buy&Hold Annualized Return'] / metrics['Buy&Hold Volatility'] \n",
    "                                        if metrics['Buy&Hold Volatility'] != 0 else 0)\n",
    "    \n",
    "    # 5. 最大回撤\n",
    "    timing_running_max = timing_cum.cummax()\n",
    "    buy_hold_running_max = buy_hold_cum.cummax()\n",
    "    metrics['Timing Max Drawdown'] = ((timing_cum - timing_running_max) / timing_running_max).min()\n",
    "    metrics['Buy&Hold Max Drawdown'] = ((buy_hold_cum - buy_hold_running_max) / buy_hold_running_max).min()\n",
    "    \n",
    "    # 6. 胜率（预测方向正确比例）\n",
    "    correct_direction = (((results_df['predicted'] > 0) & (results_df['actual'] > 0)) | \n",
    "                        ((results_df['predicted'] <= 0) & (results_df['actual'] <= 0)))\n",
    "    metrics['Hit Rate'] = correct_direction.sum() / len(results_df)\n",
    "    \n",
    "    # 7. 正收益预测准确率（处理无正预测的极端情况）\n",
    "    positive_preds = results_df['predicted'] > 0\n",
    "    metrics['Positive Prediction Accuracy'] = (results_df[positive_preds]['actual'] > 0).sum() / positive_preds.sum() \\\n",
    "        if positive_preds.sum() > 0 else 0\n",
    "    \n",
    "    return metrics\n",
    "\n",
    "# 计算并展示策略表现\n",
    "metrics = calculate_strategy_metrics(timing_results)\n",
    "\n",
    "print(\"=\"*60)\n",
    "print(\"Market Timing 策略表现\")\n",
    "print(\"=\"*60)\n",
    "for key, value in metrics.items():\n",
    "    print(f\"{key:.<45} {value:.4f}\")\n",
    "print(\"=\"*60)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
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   "source": [
    "# 可视化累计收益对比\n",
    "plt.figure(figsize=(12, 6))\n",
    "plt.plot(timing_results.index, timing_results['timing_cum'], label='Market Timing Strategy', linewidth=2)\n",
    "plt.plot(timing_results.index, timing_results['buy_hold_cum'], label='Buy & Hold Strategy', linewidth=2, alpha=0.7)\n",
    "plt.xlabel('Date', fontsize=12)\n",
    "plt.ylabel('Cumulative Wealth (Initial = 1)', fontsize=12)\n",
    "plt.title('Market Timing vs Buy & Hold: Cumulative Returns', fontsize=14, fontweight='bold')\n",
    "plt.legend(fontsize=11)\n",
    "plt.grid(True, alpha=0.3)\n",
    "plt.tight_layout()\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "====================================================================================================\n",
      "不同预测变量组合的Market Timing策略对比\n",
      "====================================================================================================\n",
      "模型              累计收益         年化收益         波动率          夏普比率         最大回撤         胜率        \n",
      "----------------------------------------------------------------------------------------------------\n",
      "RV3                  0.5951      0.0383      0.2003      0.1913     -0.4703    0.4966\n",
      "CPI                  0.4596      0.0309      0.2062      0.1499     -0.4822    0.5235\n",
      "PD                   0.8742      0.0519      0.2131      0.2435     -0.4703    0.5369\n",
      "RV3+CPI              0.5296      0.0348      0.1913      0.1820     -0.4554    0.5034\n",
      "RV3+PD               1.1783      0.0647      0.2063      0.3136     -0.4703    0.5369\n",
      "RV3+CPI+PD           0.5191      0.0343      0.2058      0.1664     -0.4822    0.5235\n",
      "----------------------------------------------------------------------------------------------------\n",
      "Buy & Hold           0.8742      0.0519      0.2131      0.2435     -0.4703       N/A\n",
      "====================================================================================================\n"
     ]
    }
   ],
   "source": [
    "# 比较不同预测变量组合的Market Timing表现\n",
    "predictor_sets = [\n",
    "    (['lRV3'], 'RV3'),\n",
    "    (['lcpi'], 'CPI'),\n",
    "    (['lpd'], 'PD'),\n",
    "    (['lRV3', 'lcpi'], 'RV3+CPI'),\n",
    "    (['lRV3', 'lpd'], 'RV3+PD'),\n",
    "    (['lRV3', 'lcpi', 'lpd'], 'RV3+CPI+PD')\n",
    "]\n",
    "\n",
    "comparison_results = {}\n",
    "\n",
    "print(\"\\n\" + \"=\"*100)\n",
    "print(\"不同预测变量组合的Market Timing策略对比\")\n",
    "print(\"=\"*100)\n",
    "print(f\"{'模型':<15} {'累计收益':<12} {'年化收益':<12} {'波动率':<12} {'夏普比率':<12} {'最大回撤':<12} {'胜率':<10}\")\n",
    "print(\"-\"*100)\n",
    "\n",
    "for predictors, name in predictor_sets:\n",
    "    results = market_timing(reg_data['2000-01':'2024-12'], 'ret', predictors, initial_sample_fraction=1/2)\n",
    "    metrics = calculate_strategy_metrics(results)\n",
    "    comparison_results[name] = {\n",
    "        'results': results,\n",
    "        'metrics': metrics\n",
    "    }\n",
    "    \n",
    "    print(f\"{name:<15} {metrics['Timing Cumulative Return']:>11.4f} {metrics['Timing Annualized Return']:>11.4f} \"\n",
    "          f\"{metrics['Timing Volatility']:>11.4f} {metrics['Timing Sharpe Ratio']:>11.4f} \"\n",
    "          f\"{metrics['Timing Max Drawdown']:>11.4f} {metrics['Hit Rate']:>9.4f}\")\n",
    "\n",
    "# Buy & Hold 基准\n",
    "buy_hold_metrics = calculate_strategy_metrics(timing_results)\n",
    "print(\"-\"*100)\n",
    "print(f\"{'Buy & Hold':<15} {buy_hold_metrics['Buy&Hold Cumulative Return']:>11.4f} \"\n",
    "      f\"{buy_hold_metrics['Buy&Hold Annualized Return']:>11.4f} \"\n",
    "      f\"{buy_hold_metrics['Buy&Hold Volatility']:>11.4f} {buy_hold_metrics['Buy&Hold Sharpe Ratio']:>11.4f} \"\n",
    "      f\"{buy_hold_metrics['Buy&Hold Max Drawdown']:>11.4f} {'N/A':>9}\")\n",
    "print(\"=\"*100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
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   "source": [
    "# 绘制所有策略的累计收益对比图\n",
    "plt.figure(figsize=(14, 8))\n",
    "\n",
    "# 绘制所有Market Timing策略\n",
    "colors = plt.cm.Set3(np.linspace(0, 1, len(predictor_sets)))\n",
    "for (predictors, name), color in zip(predictor_sets, colors):\n",
    "    results = comparison_results[name]['results']\n",
    "    plt.plot(results.index, results['timing_cum'], label=f'Timing: {name}', linewidth=2, color=color)\n",
    "\n",
    "# 绘制Buy & Hold\n",
    "plt.plot(timing_results.index, timing_results['buy_hold_cum'], \n",
    "         label='Buy & Hold', linewidth=2.5, color='black', linestyle='--', alpha=0.8)\n",
    "\n",
    "plt.xlabel('Date', fontsize=12)\n",
    "plt.ylabel('Cumulative Wealth (Initial = 1)', fontsize=12)\n",
    "plt.title('Market Timing Strategies Comparison: Different Predictor Combinations', fontsize=14, fontweight='bold')\n",
    "plt.legend(fontsize=10, loc='upper left')\n",
    "plt.grid(True, alpha=0.3)\n",
    "plt.tight_layout()\n",
    "plt.show();"
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